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A Mixed Traffic Assignment Problem and Its Upper Bound of Efficiency Loss

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  • Xiao-Jun Yu
  • Jiancheng Long

Abstract

A variational inequality (VI) formulation of a mixed traffic assignment problem associated with user equilibrium (UE) player and altruistic players (UE‐AP) is developed. The users governed by the UE player use the paths with minimum actual travel cost, while the users governed by altruistic players use the paths with minimum perceived travel cost, which is a linear combination of the actual and marginal travel costs. A nonlinear programming method is adopted to derive the efficiency loss of the UE‐AP mixed equilibrium with polynomial cost function. Finally, numerical examples are given to verify our analytical results.

Suggested Citation

  • Xiao-Jun Yu & Jiancheng Long, 2014. "A Mixed Traffic Assignment Problem and Its Upper Bound of Efficiency Loss," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:290972
    DOI: 10.1155/2014/290972
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    References listed on IDEAS

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    1. Hai Yang & Deren Han & Hong Lo, 2008. "Efficiency of Atomic Splittable Selfish Routing with Polynomial Cost Functions," Networks and Spatial Economics, Springer, vol. 8(4), pages 443-451, December.
    2. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    3. Patrick T. Harker, 1988. "Multiple Equilibrium Behaviors on Networks," Transportation Science, INFORMS, vol. 22(1), pages 39-46, February.
    4. Karakostas, George & Kim, Taeyon & Viglas, Anastasios & Xia, Hao, 2011. "On the degradation of performance for traffic networks with oblivious users," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 364-371, February.
    5. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
    6. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
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